\[ y''(x)=-\frac {y(x) (a x+b)}{4 (x-1)^2 x}-\frac {(3 x-1) y'(x)}{2 (x-1) x} \] ✓ Mathematica : cpu = 0.367353 (sec), leaf count = 510
\[\left \{\left \{y(x)\to \frac {(x-1)^{\frac {2 a \sqrt {-4 \sqrt {(4 a-1) (a+b)}-8 a-4 b+1}+2 b \left (\sqrt {-4 \sqrt {(4 a-1) (a+b)}-8 a-4 b+1}+2\right )-\sqrt {(4 a-1) (a+b)} \sqrt {-4 \sqrt {(4 a-1) (a+b)}-8 a-4 b+1}+1}{8 b+2}} \left (c_1 \, _2F_1\left (\frac {1}{4} \left (\sqrt {-8 a-4 b-4 \sqrt {(4 a-1) (a+b)}+1}+1\right ),\frac {8 \sqrt {-8 a-4 b-4 \sqrt {(4 a-1) (a+b)}+1} a+4 b \left (\sqrt {-8 a-4 b-4 \sqrt {(4 a-1) (a+b)}+1}+1\right )-4 \sqrt {(4 a-1) (a+b)} \sqrt {-8 a-4 b-4 \sqrt {(4 a-1) (a+b)}+1}-\sqrt {-8 a-4 b-4 \sqrt {(4 a-1) (a+b)}+1}+1}{16 b+4};\frac {1}{2};x\right )+i c_2 \sqrt {x} \, _2F_1\left (\frac {1}{4} \left (\sqrt {-8 a-4 b-4 \sqrt {(4 a-1) (a+b)}+1}+3\right ),\frac {8 \sqrt {-8 a-4 b-4 \sqrt {(4 a-1) (a+b)}+1} a+4 b \left (\sqrt {-8 a-4 b-4 \sqrt {(4 a-1) (a+b)}+1}+3\right )-4 \sqrt {(4 a-1) (a+b)} \sqrt {-8 a-4 b-4 \sqrt {(4 a-1) (a+b)}+1}-\sqrt {-8 a-4 b-4 \sqrt {(4 a-1) (a+b)}+1}+3}{16 b+4};\frac {3}{2};x\right )\right )}{\sqrt {1-x}}\right \}\right \}\]
✓ Maple : cpu = 0.064 (sec), leaf count = 57
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\it LegendreP} \left ( {\frac {1}{2}\sqrt {1-4\,a}}-{\frac {1}{2}},\sqrt {-a-b},\sqrt {x} \right ) +{\it \_C2}\,{\it LegendreQ} \left ( {\frac {1}{2}\sqrt {1-4\,a}}-{\frac {1}{2}},\sqrt {-a-b},\sqrt {x} \right ) \right \} \]